Sprinkle both sides of the chicken with salt and pepper. Heat olive oil in a skillet over medium high heat—choose one that can later hold the pasta.
Place chicken in the hot oil and cook for 2 minutes on each side until golden brown and cooked through. You’ll know it’s ready when it releases easily from the pan.
Transfer chicken to a plate and let it rest for 5 minutes. Slice the chicken while the pasta cooks so it stays juicy.
Pour milk and chicken broth into the skillet, add garlic, then bring the mixture to a gentle simmer. You’ll smell the garlic aroma as it heats.
Add fettuccine to the simmering liquid. Stir every 30 seconds for about 3 minutes to prevent sticking, then reduce heat to medium and stir every couple of minutes. After 9–10 minutes the pasta should be nearly tender and some liquid should still coat the bottom.
Stir in heavy cream and parmesan, then simmer for 2 minutes, stirring occasionally until the sauce thickens and the pasta is cooked. If the sauce becomes too thick, add a splash of hot tap water and toss to loosen it.
Taste and adjust salt and pepper, then serve immediately topped with parmesan and parsley.